Discontinuous Galerkin finite element approximation of quasilinear elliptic boundary value problems I: the scalar case |
| |
Authors: | Houston Paul; Robson Janice; Suli Endre |
| |
Institution: |
1 Department of Mathematics, University of Leicester, Leicester LE1 7RH, UK, 2 Computing Laboratory, University of Oxford, Wolfson Building, Parks Road, Oxford OX1 3QD, UK
|
| |
Abstract: | ** Email: Paul.Houston{at}mcs.le.ac.uk*** Email: Janice.Robson{at}comlab.ox.ac.uk**** Email: Endre.Suli{at}comlab.ox.ac.uk We develop a one-parameter family of hp-version discontinuousGalerkin finite element methods, parameterised by 1,1], for the numerical solution of quasilinear elliptic equationsin divergence form on a bounded open set d, d 2. In particular,we consider the analysis of the family for the equation ·{µ(x, |u|)u} = f(x) subject to mixed DirichletNeumannboundary conditions on . It is assumed that µ is a real-valuedfunction, µ C( x 0, )), and thereexist positive constants mµ and Mµ such that mµ(t s) µ(x, t)t µ(x, s)s Mµ(t s) for t s 0 and all x . Using a result from the theory of monotone operators for any valueof 1, 1], the corresponding method is shown to havea unique solution uDG in the finite element space. If u C1() Hk(), k 2, then with discontinuous piecewise polynomials ofdegree p 1, the error between u and uDG, measured in the brokenH1()-norm, is (hs1/pk3/2), where 1 s min {p+ 1, k}. |
| |
Keywords: | hp-finite element methods discontinuous Galerkin methods quasilinear elliptic PDEs |
本文献已被 Oxford 等数据库收录! |
|